A074651 -id:A074651 - cp's OEIS frontend

A074655 Number of Lyndon words (aperiodic necklaces) with 3n beads of 3 colors, n beads of each color.

1, 2, 14, 186, 2880, 50450, 952854, 19003474, 394394880, 8439756660, 185033201150, 4137181680698, 94020326259264, 2166105078791446, 50489825369325118, 1188777328563863850, 28236363841594782720, 675879582290807439794, 16289254212695836475436

Offset: 0

Christian G. Bower, Aug 29 2002

nonn

Index entries for sequences related to Lyndon words

Cf. A029808, A074651, A022553 (2n of 2 colors), A074656 (4n of 4 colors).

a(n) = 1/(3n) * Sum_{d|n} mu(n/d) * (3d)! / d!^3, a(0) = 1.

a(n) = A029808(n)*2 = A074651(n)/3.

a(0)=1 prepended by Alois P. Heinz, Aug 24 2015

A006174 Witt vector *3!.

Original entry on oeis.org

6, 27, 488, 7974, 149796, 2725447, 56970432, 1151053821, 25279412332, 543871341927, 12411512060544, 278163517356594, 6498314231705568, 149846653983570795, 3565206002960088128, 84045618111578025105

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074651.

More terms and formula from Christian G. Bower, Aug 28 2002

cp's OEIS Frontend

A074655 Number of Lyndon words (aperiodic necklaces) with 3n beads of 3 colors, n beads of each color.

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